The main issue therefore boils down to the problem of motion
in the potential surface with a local minimum (representing the meta-stable state) and the barrier protecting this minimum
which one should overcome to fuse two nuclei.
Taking into account the influence of the environment requires
addition of the damping force and the stochastic fluctuations.
In the case of so called: “fusion-by-diffusion” model (FBD) [1]}, the stochastic
process of shape fluctuation leads to the overcoming of the saddle point.
Fluctuating force, which is de facto caused by shape fluctuations, is assumed as a white noise
to obtain the solution of the Smoluchowski diffusion equation in the deformation space along the fission valley.
Thus, basically we touch the famous Kramers problem [2]}; the relaxation from the meta-stable state with the assumption
of the white noise and with damping proportional to the velocity.
Induced or spontaneous relaxation from the meta-stable state via fluctuating potential barriers occurs in many branches of physics:
phase transitions, bi-stability in quantum optic, spontaneous emission from excited states,
electron transport in semiconductors, kinetics of chemical reactions etc. [3]}.
